Medical imaging of metabolic and biochemical activity within a patient is known as functional imaging. Functional imaging techniques include, for example, nuclear imaging such as planar nuclear imaging, Single Photon Computed Tomography (SPECT), Positron Emission Tomography (PET), and functional computed tomography (fCT). The reconstruction of a functional image from data acquired by functional imaging is often difficult because the data can be characterized by a small signal rate and a low signal-to-noise ratio. For nuclear imaging, for example, the count rate is limited by the amount of a radioactive substance that can be administered without harming the patient. In addition, a functional image does not necessarily provide structural information. Thus, one often evaluates a functional image with the help of a structural image.
An overview of SPECT systems and PET systems as well as iterative image reconstruction for emission tomography is given in chapter 7, chapter 11, and chapter 21 of M. Wernick and J. Aarsvold, “Emission tomography: the fundamentals of PET and SPECT,” Elsevier Academic Press, 2004, the contents of which are herein incorporated by reference. An overview of different reconstruction methods is given in R. C. Puetter et al., “Digital Image Reconstruction: Deblurring and Denoising,” Annu. Rev. Astro. Astrophys., 2005, 43: 139-194, the contents of which are herein incorporated by reference.
Square root transforms and their mathematical effect on variance analysis are disclosed in M. S. Bartlett, “The square root transformation in analysis of variance,” J. Roy Stat. Soc. Suppl., 3, 68-78, 1936, F. J. Anscombe, “The transformation of Poisson, binomial and negative-binomial data,” Biometrika. 35, 236-254, 1948, and L. D. Brown and L. H. Zhao, “A test for the Poisson distribution,” Sankhya: Indian J. Stat., 64, 61 1-625, 2002. An application of a square root transform for presenting scintigraphic images is disclosed in A. H. Vija et al., “Statistically based, spatially adaptive noise reduction of planar nuclear studies.” Proc. SPIE, 5747, 634-645, 2005.